Finite Group Databasebeta

← C11×#13425 #14590618

Subgroups — C11×#13425 #14590618

Order 2816.

508 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2717C211yesmaximal, characteristic
2C2×C11×#354C211yesmaximal, characteristic
3C2×C11×#352C211yesmaximal, characteristic
4C11×#1890C211yesmaximal, characteristic
5C11×#1885C211yesmaximal, characteristic
6C11×#1867C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8C2×C11×#124C2211yescharacteristic
9C2×C11×#123C2211yescharacteristic
10C11×#518C2211yescharacteristic
11C11×#419—21no—
12C2×C11×#100C2211yescharacteristic
13C2×C11×#99C2211yescharacteristic
14C2×C11×#99C2211yescharacteristic
15C11×#397—21no—
16C11×#397—21no—
17C11×#395—21no—
18C11×#387—21no—
19C11×#386C2211yescharacteristic
20C11×#385—21no—
21C11×#385—21no—
22C11×#381—21no—
23C11×#380—21no—
24C11×#354—22no—
25C11×#352—22no—
26C11×#342—21no—
27C11×#342—21no—
28C11×#339—21no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11C2311yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C2×C11×M16—21no—
34C11×#124—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#124—21no—
38C11×#123—21no—
39C11×#123—21no—
40C11×#123—21no—
41C11×#123—21no—
42C4×D4×C11—41no—
43C4×D4×C11—41no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C11×C22⋊C4D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C11×#103—41no—
62C11×#103—41no—
63C11×#100—21no—
64C11×#100—21no—
65C11×#99—21no—
66C11×#99—21no—
67C11×#99—21no—
68C11×#99D412yes—
69C11×#95—21no—
70C11×#95—21no—
71C11×#95—21no—
72C11×#95—21no—
73C11×#95—21no—
74C11×#95—21no—
75C11×#95—41no—
76C11×#95—41no—
77C11×#95—41no—
78#13425C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11C2×D411yescharacteristic
88C2×D4×C11#4111yescharacteristic
89C2×D4×C11#4111yescharacteristic
90C2×D4×C11#4111yescharacteristic
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C11×M16—41no—
111C11×M16—41no—
112C2×C8×C11—41no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—81no—
119C11×C4⋊C4—81no—
120C11×C4⋊C4—82no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—42no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—41no—
141#2717C2×C1111yescharacteristic
142C2×#354C2×C1111yescharacteristic
143C2×#352C2×C1111yescharacteristic
144#1890C2×C1111yescharacteristic
145#1885C2×C1111yescharacteristic
146#1867C2×C1111yescharacteristic
147#1390C2×C1111yescharacteristic
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11#12011yescharacteristic
157C23×C11#12111yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12311yescharacteristic
160C23×C11#12411yescharacteristic
161Q8×C11—42no—
162Q8×C11—81no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11—81no—
200C2×C4×C11—81no—
201C2×C4×C11—81no—
202C2×C4×C11—81no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12311yescharacteristic
205C8×C11—81no—
206C2×#124C22×C1111yescharacteristic
207C2×#123C22×C1111yescharacteristic
208#518C22×C1111yescharacteristic
209#419—21no—
210C2×#100C22×C1111yescharacteristic
211C2×#99C22×C1111yescharacteristic
212C2×#99C22×C1111yescharacteristic
213#397—21no—
214#397—21no—
215#395—21no—
216#387—21no—
217#386C22×C1111yescharacteristic
218#385—21no—
219#385—21no—
220#381—21no—
221#380—21no—
222#354—22no—
223#352—22no—
224#342—21no—
225#342—21no—
226#339—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#39411yescharacteristic
244C22×C11B(4,𝔽2)11yescharacteristic
245C22×C11#45811yescharacteristic
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—42no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—82no—
253C4×C11—81no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11—161no—
258C22×Q8D4×C1111yescharacteristic
259C22×D4C23×C1111yescharacteristic
260C23×C4D4×C1111yescharacteristic
261C23×C4D4×C1111yescharacteristic
262C2×M16—21no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271C4×D4—41no—
272C4×D4—41no—
273#117—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—41no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4D4×C1111yescharacteristic
288C2×C22⋊C4D4×C1111yescharacteristic
289C2×C42D4×C1111yescharacteristic
290#103—41no—
291#103—41no—
292#100—21no—
293#100—21no—
294#99—21no—
295#99—21no—
296#99—21no—
297#99D4×C1112yes—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—41no—
305#95—41no—
306#95—41no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—41no—
310C2×C11—41no—
311C2×C11—41no—
312C2×C11—41no—
313C2×C11#204411yescharacteristic
314C2×C11#219711yescharacteristic
315C2×C11#220111yescharacteristic
316C24C2×D4×C1111yescharacteristic
317C24C2×D4×C1111yescharacteristic
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4C2×D4×C1111yescharacteristic
325C2×D4C11×#4111yescharacteristic
326C2×D4C11×#4111yescharacteristic
327C2×D4C11×#4111yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4C2×D4×C1111yescharacteristic
347M16—41no—
348M16—41no—
349C2×C8—41no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—42no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—81no—
356C4⋊C4—81no—
357C4⋊C4—82no—
358C22⋊C4—22no—
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—42no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C42—21no—
376C42—21no—
377C42—41no—
378C11#1342511yescharacteristic, direct product factor, Sylow
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C11×#12011yescharacteristic
388C23C11×#12111yescharacteristic
389C23C11×#12111yescharacteristic
390C23C11×#12311yescharacteristic
391C23C11×#12411yescharacteristic
392Q8—42no—
393Q8—81no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4C11×#12111yescharacteristic
435C2×C4C11×#12311yescharacteristic
436C8—81no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22C11×#39411yescharacteristic
454C22C11×B(4,𝔽2)11yescharacteristic
455C22C11×#45811yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—82no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4—81no—
467C4—161no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2C11×#204411yescharacteristic
475C2C11×#219711yescharacteristic
476C2C11×#220111yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
78. #13425C11direct (N × H)
378. C11#13425direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#27172
C2×C11×#3542
C2×C11×#3522
C11×#18902
C11×#18852
C11×#18672
C11×#13902
#1342511